19.10 problem 10

Internal problem ID [10603]

Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section: Chapter 1, section 1.2. Riccati Equation. subsection 1.2.8-1. Equations containing arbitrary functions (but not containing their derivatives).
Problem number: 10.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_Riccati]

\[ \boxed {y^{\prime }-y^{2} f \left (x \right )-g \left (x \right ) y=a n \,x^{n -1}-a \,x^{n} g \left (x \right )-a^{2} x^{2 n} f \left (x \right )} \]

✗ Solution by Maple

dsolve(diff(y(x),x)=f(x)*y(x)^2+g(x)*y(x)+a*n*x^(n-1)-a*x^n*g(x)-a^2*f(x)*x^(2*n),y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.0 (sec). Leaf size: 0

DSolve[y'[x]==f[x]*y[x]^2+g[x]*y[x]+a*n*x^(n-1)-a*x^n*g[x]-a^2*f[x]*x^(2*n),y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved